MinT - Best Known (198−114, 198, s)-Nets in Base 4

Best Known (198−114, 198, s)-Nets in Base 4

(198−114, 198, 104)-Net over F₄ — Constructive and digital

Digital (84, 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]

(198−114, 198, 129)-Net over F₄ — Digital

Digital (84, 198, 129)-net over F₄, using

t-expansion [i] based on 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]

(198−114, 198, 862)-Net in Base 4 — Upper bound on s

There is no (84, 198, 863)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169402 462596 357962 005827 499525 081633 448205 866789 388254 514247 576086 924382 981119 252528 878059 365074 831663 566669 772076 010420 > 4¹⁹⁸ [i]