MinT - Best Known (117, 117+143, s)-Nets in Base 4

Best Known (117, 117+143, s)-Nets in Base 4

(117, 117+143, 130)-Net over F₄ — Constructive and digital

Digital (117, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(117, 117+143, 168)-Net over F₄ — Digital

Digital (117, 260, 168)-net over F₄, using

t-expansion [i] based on digital (115, 260, 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]

(117, 117+143, 1370)-Net in Base 4 — Upper bound on s

There is no (117, 260, 1371)-net in base 4, because

1 times m-reduction [i] would yield (117, 259, 1371)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 887560 379416 821039 272682 429086 352180 553709 912270 003559 087076 645647 664918 428127 094840 370040 283440 275209 176701 674017 159156 146794 179252 838589 687122 149471 438144 > 4²⁵⁹ [i]