MinT - Best Known (207−133, 207, s)-Nets in Base 4

Best Known (207−133, 207, s)-Nets in Base 4

(207−133, 207, 104)-Net over F₄ — Constructive and digital

Digital (74, 207, 104)-net over F₄, using

t-expansion [i] based on digital (73, 207, 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]

(207−133, 207, 112)-Net over F₄ — Digital

Digital (74, 207, 112)-net over F₄, using

t-expansion [i] based on digital (73, 207, 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]

(207−133, 207, 588)-Net in Base 4 — Upper bound on s

There is no (74, 207, 589)-net in base 4, because

1 times m-reduction [i] would yield (74, 206, 589)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11037 406247 324343 144946 043609 304129 235374 392925 529895 432469 139245 796773 364857 186612 580848 903155 080291 624896 807973 752470 489410 > 4²⁰⁶ [i]