MinT - Best Known (98, 98+89, s)-Nets in Base 3

Best Known (98, 98+89, s)-Nets in Base 3

(98, 98+89, 74)-Net over F₃ — Constructive and digital

Digital (98, 187, 74)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 71, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. digital (27, 116, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(98, 98+89, 109)-Net over F₃ — Digital

Digital (98, 187, 109)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+89, 854)-Net in Base 3 — Upper bound on s

There is no (98, 187, 855)-net in base 3, because

1 times m-reduction [i] would yield (98, 186, 855)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57185 734007 406816 629658 318315 613708 395225 211994 877511 172888 621615 306169 989982 124134 551977 > 3¹⁸⁶ [i]