MinT - Best Known (248−132, 248, s)-Nets in Base 4

Best Known (248−132, 248, s)-Nets in Base 4

(248−132, 248, 130)-Net over F₄ — Constructive and digital

Digital (116, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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]

(248−132, 248, 168)-Net over F₄ — Digital

Digital (116, 248, 168)-net over F₄, using

t-expansion [i] based on digital (115, 248, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(248−132, 248, 1495)-Net in Base 4 — Upper bound on s

There is no (116, 248, 1496)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 205106 006622 425182 058519 437993 018178 552376 440326 581509 963701 053782 788296 443826 411473 231255 760482 297494 326871 534342 918301 249375 686723 069341 638617 724899 > 4²⁴⁸ [i]