MinT - Best Known (112, 112+137, s)-Nets in Base 4

Best Known (112, 112+137, s)-Nets in Base 4

(112, 112+137, 130)-Net over F₄ — Constructive and digital

Digital (112, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(112, 112+137, 165)-Net over F₄ — Digital

Digital (112, 249, 165)-net over F₄, using

t-expansion [i] based on digital (109, 249, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(112, 112+137, 1313)-Net in Base 4 — Upper bound on s

There is no (112, 249, 1314)-net in base 4, because

1 times m-reduction [i] would yield (112, 248, 1314)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214691 436206 073344 942524 153721 154486 526832 226585 017847 456543 184317 960433 740415 666763 553831 208205 722767 341725 766360 914949 746596 557623 958462 810438 795680 > 4²⁴⁸ [i]