MinT - Best Known (217−122, 217, s)-Nets in Base 4

Best Known (217−122, 217, s)-Nets in Base 4

(217−122, 217, 104)-Net over F₄ — Constructive and digital

Digital (95, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(217−122, 217, 144)-Net over F₄ — Digital

Digital (95, 217, 144)-net over F₄, using

t-expansion [i] based on digital (91, 217, 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]

(217−122, 217, 1039)-Net in Base 4 — Upper bound on s

There is no (95, 217, 1040)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46658 099848 877939 068995 409850 715166 169062 969158 428215 308364 730753 799624 286231 080424 151831 838711 957554 873197 510244 297334 497328 036160 > 4²¹⁷ [i]