MinT - Best Known (198−124, 198, s)-Nets in Base 4

Best Known (198−124, 198, s)-Nets in Base 4

(198−124, 198, 104)-Net over F₄ — Constructive and digital

Digital (74, 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]

(198−124, 198, 112)-Net over F₄ — Digital

Digital (74, 198, 112)-net over F₄, using

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

(198−124, 198, 617)-Net in Base 4 — Upper bound on s

There is no (74, 198, 618)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161713 142003 384253 166593 792390 141950 705138 815599 709487 338479 142687 562150 762867 681254 152395 150615 538435 559975 313053 333600 > 4¹⁹⁸ [i]