MinT - Best Known (88, 251, s)-Nets in Base 4

Best Known (88, 251, s)-Nets in Base 4

(88, 251, 104)-Net over F₄ — Constructive and digital

Digital (88, 251, 104)-net over F₄, using

t-expansion [i] based on digital (73, 251, 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]

(88, 251, 129)-Net over F₄ — Digital

Digital (88, 251, 129)-net over F₄, using

t-expansion [i] based on digital (81, 251, 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]

(88, 251, 679)-Net in Base 4 — Upper bound on s

There is no (88, 251, 680)-net in base 4, because

1 times m-reduction [i] would yield (88, 250, 680)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 303961 265441 513913 364426 842918 349517 797851 962974 759323 224617 966654 711124 155635 688255 097375 792755 422119 912530 347205 886042 257926 068873 178142 308747 407860 > 4²⁵⁰ [i]