MinT - Best Known (113, 113+129, s)-Nets in Base 4

Best Known (113, 113+129, s)-Nets in Base 4

(113, 113+129, 130)-Net over F₄ — Constructive and digital

Digital (113, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(113, 113+129, 165)-Net over F₄ — Digital

Digital (113, 242, 165)-net over F₄, using

t-expansion [i] based on digital (109, 242, 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]

(113, 113+129, 1469)-Net in Base 4 — Upper bound on s

There is no (113, 242, 1470)-net in base 4, because

1 times m-reduction [i] would yield (113, 241, 1470)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 868795 204922 657532 906257 142938 081004 215369 426403 697235 020236 435224 439352 218499 666383 948128 584994 072727 175949 012064 308462 902668 426369 635927 176030 > 4²⁴¹ [i]