MinT - Best Known (91, 91+33, s)-Nets in Base 3

Best Known (91, 91+33, s)-Nets in Base 3

(91, 91+33, 252)-Net over F₃ — Constructive and digital

Digital (91, 124, 252)-net over F₃, using

3¹ times duplication [i] based on digital (90, 123, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 41, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(91, 91+33, 460)-Net over F₃ — Digital

Digital (91, 124, 460)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+33, 15810)-Net in Base 3 — Upper bound on s

There is no (91, 124, 15811)-net in base 3, because

1 times m-reduction [i] would yield (91, 123, 15811)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48530 599954 896355 325581 583286 386829 378588 340576 691471 183073 > 3¹²³ [i]