MinT - Best Known (75, 75+122, s)-Nets in Base 4

Best Known (75, 75+122, s)-Nets in Base 4

(75, 75+122, 104)-Net over F₄ — Constructive and digital

Digital (75, 197, 104)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(75, 75+122, 112)-Net over F₄ — Digital

Digital (75, 197, 112)-net over F₄, using

t-expansion [i] based on digital (73, 197, 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]

(75, 75+122, 641)-Net in Base 4 — Upper bound on s

There is no (75, 197, 642)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40405 946788 269917 510723 508083 577176 089910 389871 771770 182513 594565 353261 441225 609685 321846 467700 595252 648794 552325 177440 > 4¹⁹⁷ [i]