MinT - Best Known (79, 79+108, s)-Nets in Base 4

Best Known (79, 79+108, s)-Nets in Base 4

(79, 79+108, 104)-Net over F₄ — Constructive and digital

Digital (79, 187, 104)-net over F₄, using

t-expansion [i] based on digital (73, 187, 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]

(79, 79+108, 112)-Net over F₄ — Digital

Digital (79, 187, 112)-net over F₄, using

t-expansion [i] based on digital (73, 187, 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]

(79, 79+108, 806)-Net in Base 4 — Upper bound on s

There is no (79, 187, 807)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40488 329677 165847 311268 842287 300224 179914 097887 751779 640857 425422 755687 520735 755656 581621 558974 143718 896259 794032 > 4¹⁸⁷ [i]