MinT - Best Known (102, 102+118, s)-Nets in Base 4

Best Known (102, 102+118, s)-Nets in Base 4

(102, 102+118, 104)-Net over F₄ — Constructive and digital

Digital (102, 220, 104)-net over F₄, using

t-expansion [i] based on digital (73, 220, 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]

(102, 102+118, 144)-Net over F₄ — Digital

Digital (102, 220, 144)-net over F₄, using

t-expansion [i] based on digital (91, 220, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(102, 102+118, 1289)-Net in Base 4 — Upper bound on s

There is no (102, 220, 1290)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 945083 573899 995317 097188 829074 765495 509820 766033 625840 942721 189412 101372 854559 696936 565023 330017 953749 373232 855910 769831 301686 811520 > 4²²⁰ [i]