MinT - Best Known (247−125, 247, s)-Nets in Base 4

Best Known (247−125, 247, s)-Nets in Base 4

(247−125, 247, 130)-Net over F₄ — Constructive and digital

Digital (122, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(247−125, 247, 168)-Net over F₄ — Digital

Digital (122, 247, 168)-net over F₄, using

t-expansion [i] based on digital (115, 247, 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]

(247−125, 247, 1902)-Net in Base 4 — Upper bound on s

There is no (122, 247, 1903)-net in base 4, because

1 times m-reduction [i] would yield (122, 246, 1903)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13070 179595 650771 895344 610015 309230 142839 112977 464610 116103 936819 610533 745596 394114 069390 344427 354112 873747 145178 073369 174248 181958 149294 138949 328740 > 4²⁴⁶ [i]