MinT - Best Known (258−170, 258, s)-Nets in Base 4

Best Known (258−170, 258, s)-Nets in Base 4

(258−170, 258, 104)-Net over F₄ — Constructive and digital

Digital (88, 258, 104)-net over F₄, using

t-expansion [i] based on digital (73, 258, 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]

(258−170, 258, 129)-Net over F₄ — Digital

Digital (88, 258, 129)-net over F₄, using

t-expansion [i] based on digital (81, 258, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(258−170, 258, 659)-Net in Base 4 — Upper bound on s

There is no (88, 258, 660)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 239823 182887 964594 011617 466795 762738 081990 487992 725471 723089 340999 065202 789586 563948 722347 994862 118921 420093 200084 320255 142464 495313 829591 913196 413047 061920 > 4²⁵⁸ [i]