MinT - Best Known (188−130, 188, s)-Nets in Base 4

Best Known (188−130, 188, s)-Nets in Base 4

(188−130, 188, 66)-Net over F₄ — Constructive and digital

Digital (58, 188, 66)-net over F₄, using

t-expansion [i] based on digital (49, 188, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(188−130, 188, 91)-Net over F₄ — Digital

Digital (58, 188, 91)-net over F₄, using

t-expansion [i] based on digital (50, 188, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(188−130, 188, 408)-Net in Base 4 — Upper bound on s

There is no (58, 188, 409)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 158929 228509 443566 752609 985149 044607 123741 483930 378871 429143 417185 337465 510648 172119 945326 954966 159574 317471 545720 > 4¹⁸⁸ [i]