MinT - Best Known (98, 98+87, s)-Nets in Base 3

Best Known (98, 98+87, s)-Nets in Base 3

(98, 98+87, 74)-Net over F₃ — Constructive and digital

Digital (98, 185, 74)-net over F₃, using

1 times m-reduction [i] based on digital (98, 186, 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, 115, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(98, 98+87, 111)-Net over F₃ — Digital

Digital (98, 185, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+87, 887)-Net in Base 3 — Upper bound on s

There is no (98, 185, 888)-net in base 3, because

1 times m-reduction [i] would yield (98, 184, 888)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6339 720765 158740 435202 650189 898170 061068 916803 856022 698221 087380 302951 534282 383949 025633 > 3¹⁸⁴ [i]