MinT - Best Known (199−120, 199, s)-Nets in Base 4

Best Known (199−120, 199, s)-Nets in Base 4

(199−120, 199, 104)-Net over F₄ — Constructive and digital

Digital (79, 199, 104)-net over F₄, using

t-expansion [i] based on digital (73, 199, 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]

(199−120, 199, 112)-Net over F₄ — Digital

Digital (79, 199, 112)-net over F₄, using

t-expansion [i] based on digital (73, 199, 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]

(199−120, 199, 719)-Net in Base 4 — Upper bound on s

There is no (79, 199, 720)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 691315 140092 909960 429763 514262 064175 614896 108076 850666 355493 199961 960458 216946 011419 348908 385363 468170 817439 452576 010180 > 4¹⁹⁹ [i]