MinT - Best Known (33, 33+39, s)-Nets in Base 32

Best Known (33, 33+39, s)-Nets in Base 32

(33, 33+39, 196)-Net over F₃₂ — Constructive and digital

Digital (33, 72, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 26, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (7, 46, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(33, 33+39, 288)-Net in Base 32 — Constructive

(33, 72, 288)-net in base 32, using

12 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(33, 33+39, 350)-Net over F₃₂ — Digital

Digital (33, 72, 350)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(33, 33+39, 107726)-Net in Base 32 — Upper bound on s

There is no (33, 72, 107727)-net in base 32, because

1 times m-reduction [i] would yield (33, 71, 107727)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 73397 384591 461995 197089 670050 080644 315551 295382 535077 472191 629438 670499 764801 210621 944807 518736 524603 474864 > 32⁷¹ [i]