MinT - Best Known (256−158, 256, s)-Nets in Base 4

Best Known (256−158, 256, s)-Nets in Base 4

(256−158, 256, 104)-Net over F₄ — Constructive and digital

Digital (98, 256, 104)-net over F₄, using

t-expansion [i] based on digital (73, 256, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(256−158, 256, 144)-Net over F₄ — Digital

Digital (98, 256, 144)-net over F₄, using

t-expansion [i] based on digital (91, 256, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(256−158, 256, 836)-Net in Base 4 — Upper bound on s

There is no (98, 256, 837)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 14081 453970 179399 289298 440039 091405 162551 325384 508134 838194 336334 641829 356968 250553 699451 705192 750161 604856 058420 912186 682481 446556 196658 510169 743233 267968 > 4²⁵⁶ [i]