MinT - Best Known (98, 98+45, s)-Nets in Base 3

Best Known (98, 98+45, s)-Nets in Base 3

(98, 98+45, 156)-Net over F₃ — Constructive and digital

Digital (98, 143, 156)-net over F₃, using

9 times m-reduction [i] based on digital (98, 152, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 76, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(98, 98+45, 286)-Net over F₃ — Digital

Digital (98, 143, 286)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+45, 5416)-Net in Base 3 — Upper bound on s

There is no (98, 143, 5417)-net in base 3, because

1 times m-reduction [i] would yield (98, 142, 5417)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 542096 126916 871715 596681 284760 499728 650419 964047 232031 559428 218793 > 3¹⁴² [i]