MinT - Best Known (46, 77, s)-Nets in Base 27

Best Known (46, 77, s)-Nets in Base 27

(46, 77, 246)-Net over F₂₇ — Constructive and digital

Digital (46, 77, 246)-net over F₂₇, using

generalized (u,Â u+v)-construction [i] based on
1. digital (7, 17, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]
2. digital (7, 22, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇ (see above)
3. digital (7, 38, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇ (see above)

(46, 77, 370)-Net in Base 27 — Constructive

(46, 77, 370)-net in base 27, using

t-expansion [i] based on (43, 77, 370)-net in base 27, using
- 31 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
  - base change [i] based on digital (16, 81, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(46, 77, 2201)-Net over F₂₇ — Digital

Digital (46, 77, 2201)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 77, 4416066)-Net in Base 27 — Upper bound on s

There is no (46, 77, 4416067)-net in base 27, because

1 times m-reduction [i] would yield (46, 76, 4416067)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 6 076403 330247 979514 124041 777730 333509 369154 454188 867842 668993 654636 521942 662717 566151 787901 968270 142904 126763 > 27⁷⁶ [i]