MinT - Best Known (102, 102+138, s)-Nets in Base 4

Best Known (102, 102+138, s)-Nets in Base 4

(102, 102+138, 104)-Net over F₄ — Constructive and digital

Digital (102, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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+138, 144)-Net over F₄ — Digital

Digital (102, 240, 144)-net over F₄, using

t-expansion [i] based on digital (91, 240, 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+138, 1042)-Net in Base 4 — Upper bound on s

There is no (102, 240, 1043)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 267450 838491 666908 315618 577971 471387 911657 486246 945427 640492 165855 104514 261268 963342 948867 676572 579026 370869 569414 414373 462460 408917 606021 174400 > 4²⁴⁰ [i]