MinT - Best Known (244−129, 244, s)-Nets in Base 4

Best Known (244−129, 244, s)-Nets in Base 4

(244−129, 244, 130)-Net over F₄ — Constructive and digital

Digital (115, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(244−129, 244, 168)-Net over F₄ — Digital

Digital (115, 244, 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]

(244−129, 244, 1536)-Net in Base 4 — Upper bound on s

There is no (115, 244, 1537)-net in base 4, because

1 times m-reduction [i] would yield (115, 243, 1537)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 202 915930 523229 030157 811702 502808 432228 438288 675344 200463 993098 492390 650401 034678 990850 284698 922957 874092 289642 077831 003184 373108 977719 697537 816680 > 4²⁴³ [i]