MinT - Best Known (124, 124+129, s)-Nets in Base 4

Best Known (124, 124+129, s)-Nets in Base 4

(124, 124+129, 130)-Net over F₄ — Constructive and digital

Digital (124, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(124, 124+129, 168)-Net over F₄ — Digital

Digital (124, 253, 168)-net over F₄, using

t-expansion [i] based on digital (115, 253, 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]

(124, 124+129, 1878)-Net in Base 4 — Upper bound on s

There is no (124, 253, 1879)-net in base 4, because

1 times m-reduction [i] would yield (124, 252, 1879)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53 280715 400958 508360 664230 032645 505148 621502 189685 303801 125570 736971 913196 879033 816066 257064 177676 484654 862208 934567 739159 953706 247059 952581 236891 836769 > 4²⁵² [i]