MinT - Best Known (118, 118+129, s)-Nets in Base 4

Best Known (118, 118+129, s)-Nets in Base 4

(118, 118+129, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(118, 118+129, 168)-Net over F₄ — Digital

Digital (118, 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]

(118, 118+129, 1643)-Net in Base 4 — Upper bound on s

There is no (118, 247, 1644)-net in base 4, because

1 times m-reduction [i] would yield (118, 246, 1644)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13155 873053 238910 055858 061681 487342 470182 759217 450174 139075 037210 945748 096070 783803 275166 452785 511465 223317 613396 796079 456876 114477 730980 872287 148015 > 4²⁴⁶ [i]