MinT - Best Known (250−140, 250, s)-Nets in Base 4

Best Known (250−140, 250, s)-Nets in Base 4

(250−140, 250, 130)-Net over F₄ — Constructive and digital

Digital (110, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(250−140, 250, 165)-Net over F₄ — Digital

Digital (110, 250, 165)-net over F₄, using

t-expansion [i] based on digital (109, 250, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(250−140, 250, 1210)-Net in Base 4 — Upper bound on s

There is no (110, 250, 1211)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 426352 926314 814394 185349 744699 859244 288793 346149 443553 268429 675705 685935 902122 083052 785825 441524 457465 740935 134127 775742 839934 638714 023521 267883 410380 > 4²⁵⁰ [i]