MinT - Best Known (128, 186, s)-Nets in Base 3

Best Known (128, 186, s)-Nets in Base 3

(128, 186, 192)-Net over F₃ — Constructive and digital

Digital (128, 186, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 62, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(128, 186, 368)-Net over F₃ — Digital

Digital (128, 186, 368)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 186, 6674)-Net in Base 3 — Upper bound on s

There is no (128, 186, 6675)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55716 384494 578649 533320 361358 875777 822611 459665 013678 696172 200776 400008 578670 160678 008495 > 3¹⁸⁶ [i]