MinT - Best Known (198−117, 198, s)-Nets in Base 4

Best Known (198−117, 198, s)-Nets in Base 4

(198−117, 198, 104)-Net over F₄ — Constructive and digital

Digital (81, 198, 104)-net over F₄, using

t-expansion [i] based on digital (73, 198, 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]

(198−117, 198, 129)-Net over F₄ — Digital

Digital (81, 198, 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]

(198−117, 198, 783)-Net in Base 4 — Upper bound on s

There is no (81, 198, 784)-net in base 4, because

1 times m-reduction [i] would yield (81, 197, 784)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42955 099361 825134 092574 763391 945870 205595 316489 523876 754845 975098 579935 474416 258092 667027 398382 703064 167839 041974 787760 > 4¹⁹⁷ [i]