MinT - Best Known (253−134, 253, s)-Nets in Base 4

Best Known (253−134, 253, s)-Nets in Base 4

(253−134, 253, 130)-Net over F₄ — Constructive and digital

Digital (119, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(253−134, 253, 168)-Net over F₄ — Digital

Digital (119, 253, 168)-net over F₄, using

t-expansion [i] based on digital (115, 253, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(253−134, 253, 1558)-Net in Base 4 — Upper bound on s

There is no (119, 253, 1559)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212 759951 866590 723697 101344 834896 725709 046831 486529 239045 852414 918818 626046 909976 025767 908898 418976 324588 337347 733355 628357 598964 232765 893712 273321 408000 > 4²⁵³ [i]