MinT - Best Known (248−134, 248, s)-Nets in Base 4

Best Known (248−134, 248, s)-Nets in Base 4

(248−134, 248, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(248−134, 248, 165)-Net over F₄ — Digital

Digital (114, 248, 165)-net over F₄, using

t-expansion [i] based on digital (109, 248, 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]

(248−134, 248, 1400)-Net in Base 4 — Upper bound on s

There is no (114, 248, 1401)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212770 142000 271688 353944 656853 335886 011699 749680 892033 745972 699083 910938 305929 201962 539491 449767 475791 820409 248897 522142 382769 166412 503931 801640 266680 > 4²⁴⁸ [i]