MinT - Best Known (97, 259, s)-Nets in Base 4

Best Known (97, 259, s)-Nets in Base 4

(97, 259, 104)-Net over F₄ — Constructive and digital

Digital (97, 259, 104)-net over F₄, using

t-expansion [i] based on digital (73, 259, 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]

(97, 259, 144)-Net over F₄ — Digital

Digital (97, 259, 144)-net over F₄, using

t-expansion [i] based on digital (91, 259, 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]

(97, 259, 803)-Net in Base 4 — Upper bound on s

There is no (97, 259, 804)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 888224 891653 092540 969927 267870 537411 629691 450548 675872 598440 303929 292197 477124 908095 084715 903217 266315 517773 980571 532475 758061 451261 854868 573681 450268 963480 > 4²⁵⁹ [i]