MinT - Best Known (249−136, 249, s)-Nets in Base 4

Best Known (249−136, 249, s)-Nets in Base 4

(249−136, 249, 130)-Net over F₄ — Constructive and digital

Digital (113, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(249−136, 249, 165)-Net over F₄ — Digital

Digital (113, 249, 165)-net over F₄, using

t-expansion [i] based on digital (109, 249, 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]

(249−136, 249, 1341)-Net in Base 4 — Upper bound on s

There is no (113, 249, 1342)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 851061 582219 802741 839665 449822 762369 366994 650357 898661 851320 089202 839771 098400 746917 717383 300669 773097 306063 657628 818571 207619 112182 408236 826704 743820 > 4²⁴⁹ [i]