MinT - Best Known (237−130, 237, s)-Nets in Base 4

Best Known (237−130, 237, s)-Nets in Base 4

(237−130, 237, 130)-Net over F₄ — Constructive and digital

Digital (107, 237, 130)-net over F₄, using

t-expansion [i] based on digital (105, 237, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(237−130, 237, 144)-Net over F₄ — Digital

Digital (107, 237, 144)-net over F₄, using

t-expansion [i] based on digital (91, 237, 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]

(237−130, 237, 1255)-Net in Base 4 — Upper bound on s

There is no (107, 237, 1256)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49461 268440 218948 508242 129091 257900 595565 707319 902795 208614 703244 892949 928924 418825 028386 716918 513409 740571 412707 561452 962116 343158 109989 913633 > 4²³⁷ [i]