MinT - Best Known (231−140, 231, s)-Nets in Base 4

Best Known (231−140, 231, s)-Nets in Base 4

(231−140, 231, 104)-Net over F₄ — Constructive and digital

Digital (91, 231, 104)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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]

(231−140, 231, 144)-Net over F₄ — Digital

Digital (91, 231, 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]

(231−140, 231, 813)-Net in Base 4 — Upper bound on s

There is no (91, 231, 814)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 617217 754135 053044 280149 359856 449312 103820 576595 018019 164694 749261 537369 712737 068323 623679 982182 318580 301122 764432 400651 194562 026597 431888 > 4²³¹ [i]