MinT - Best Known (243−126, 243, s)-Nets in Base 4

Best Known (243−126, 243, s)-Nets in Base 4

(243−126, 243, 130)-Net over F₄ — Constructive and digital

Digital (117, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(243−126, 243, 168)-Net over F₄ — Digital

Digital (117, 243, 168)-net over F₄, using

t-expansion [i] based on digital (115, 243, 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]

(243−126, 243, 1649)-Net in Base 4 — Upper bound on s

There is no (117, 243, 1650)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 200 561600 481278 287755 238013 245013 546827 732074 525799 159126 740954 097382 787126 047512 916677 979045 076261 484654 043282 251012 889210 715080 146425 426267 419296 > 4²⁴³ [i]