MinT - Best Known (253−156, 253, s)-Nets in Base 4

Best Known (253−156, 253, s)-Nets in Base 4

(253−156, 253, 104)-Net over F₄ — Constructive and digital

Digital (97, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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]

(253−156, 253, 144)-Net over F₄ — Digital

Digital (97, 253, 144)-net over F₄, using

t-expansion [i] based on digital (91, 253, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(253−156, 253, 830)-Net in Base 4 — Upper bound on s

There is no (97, 253, 831)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 227 919950 774216 198478 537108 266516 201801 959734 204510 338337 666162 573724 310524 481714 989540 622488 438209 632305 177557 407133 733617 880228 237147 218240 479450 775508 > 4²⁵³ [i]