MinT - Best Known (97, 97+122, s)-Nets in Base 4

Best Known (97, 97+122, s)-Nets in Base 4

(97, 97+122, 104)-Net over F₄ — Constructive and digital

Digital (97, 219, 104)-net over F₄, using

t-expansion [i] based on digital (73, 219, 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]

(97, 97+122, 144)-Net over F₄ — Digital

Digital (97, 219, 144)-net over F₄, using

t-expansion [i] based on digital (91, 219, 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]

(97, 97+122, 1089)-Net in Base 4 — Upper bound on s

There is no (97, 219, 1090)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 722006 947437 894207 407157 667426 063440 933794 868599 871303 163320 480922 972743 598382 873817 891981 828202 753317 683945 542578 086338 596851 849680 > 4²¹⁹ [i]