MinT - Best Known (245−126, 245, s)-Nets in Base 4

Best Known (245−126, 245, s)-Nets in Base 4

(245−126, 245, 130)-Net over F₄ — Constructive and digital

Digital (119, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(245−126, 245, 168)-Net over F₄ — Digital

Digital (119, 245, 168)-net over F₄, using

t-expansion [i] based on digital (115, 245, 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]

(245−126, 245, 1726)-Net in Base 4 — Upper bound on s

There is no (119, 245, 1727)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3263 535602 568131 270946 210420 759392 533911 149047 051553 012406 596718 476714 035609 000074 186648 269202 267833 710867 337957 341058 624445 449122 100626 322184 095788 > 4²⁴⁵ [i]