MinT - Best Known (88, 194, s)-Nets in Base 4

Best Known (88, 194, s)-Nets in Base 4

(88, 194, 104)-Net over F₄ — Constructive and digital

Digital (88, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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, 194, 129)-Net over F₄ — Digital

Digital (88, 194, 129)-net over F₄, using

t-expansion [i] based on digital (81, 194, 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, 194, 1054)-Net in Base 4 — Upper bound on s

There is no (88, 194, 1055)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 643 822161 448571 019664 974206 207781 526721 790633 325013 042451 460926 752583 918310 734994 970862 928605 448634 999083 761164 605888 > 4¹⁹⁴ [i]