MinT - Best Known (247−127, 247, s)-Nets in Base 4

Best Known (247−127, 247, s)-Nets in Base 4

(247−127, 247, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(247−127, 247, 168)-Net over F₄ — Digital

Digital (120, 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]

(247−127, 247, 1765)-Net in Base 4 — Upper bound on s

There is no (120, 247, 1766)-net in base 4, because

1 times m-reduction [i] would yield (120, 246, 1766)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12805 272574 551578 917155 077828 708074 466491 757631 044159 282131 575343 445163 440950 628572 752908 093000 552378 152890 666106 057296 086215 254523 267878 946651 267360 > 4²⁴⁶ [i]