MinT - Best Known (208−119, 208, s)-Nets in Base 4

Best Known (208−119, 208, s)-Nets in Base 4

(208−119, 208, 104)-Net over F₄ — Constructive and digital

Digital (89, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−119, 208, 129)-Net over F₄ — Digital

Digital (89, 208, 129)-net over F₄, using

t-expansion [i] based on digital (81, 208, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(208−119, 208, 937)-Net in Base 4 — Upper bound on s

There is no (89, 208, 938)-net in base 4, because

1 times m-reduction [i] would yield (89, 207, 938)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43745 949286 101505 138037 824120 319314 042217 577077 182890 344896 770051 259261 721695 048094 634947 544274 606006 202834 805573 308707 441600 > 4²⁰⁷ [i]