MinT - Best Known (232−65, 232, s)-Nets in Base 3

Best Known (232−65, 232, s)-Nets in Base 3

(232−65, 232, 288)-Net over F₃ — Constructive and digital

Digital (167, 232, 288)-net over F₃, using

2 times m-reduction [i] based on digital (167, 234, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 78, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(232−65, 232, 632)-Net over F₃ — Digital

Digital (167, 232, 632)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−65, 232, 17754)-Net in Base 3 — Upper bound on s

There is no (167, 232, 17755)-net in base 3, because

1 times m-reduction [i] would yield (167, 231, 17755)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 310687 396460 743414 312836 108409 140832 058987 952100 757546 207243 617096 097822 717531 490068 932489 165564 157370 099649 > 3²³¹ [i]