MinT - Best Known (253−174, 253, s)-Nets in Base 4

Best Known (253−174, 253, s)-Nets in Base 4

(253−174, 253, 104)-Net over F₄ — Constructive and digital

Digital (79, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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]

(253−174, 253, 112)-Net over F₄ — Digital

Digital (79, 253, 112)-net over F₄, using

t-expansion [i] based on digital (73, 253, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(253−174, 253, 554)-Net in Base 4 — Upper bound on s

There is no (79, 253, 555)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 233 078789 888786 098250 915735 531423 957859 973710 098499 460188 743955 235026 782811 521464 207520 348160 690190 924498 620515 518689 199013 233942 557893 968651 235626 009600 > 4²⁵³ [i]