MinT - Best Known (98, 180, s)-Nets in Base 3

Best Known (98, 180, s)-Nets in Base 3

(98, 180, 80)-Net over F₃ — Constructive and digital

Digital (98, 180, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 90, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(98, 180, 119)-Net over F₃ — Digital

Digital (98, 180, 119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 180, 963)-Net in Base 3 — Upper bound on s

There is no (98, 180, 964)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 898698 639015 014780 236190 929589 075584 861160 471280 250768 526989 077358 502130 687439 010441 > 3¹⁸⁰ [i]