MinT - Best Known (113, 113+140, s)-Nets in Base 4

Best Known (113, 113+140, s)-Nets in Base 4

(113, 113+140, 130)-Net over F₄ — Constructive and digital

Digital (113, 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]

(113, 113+140, 165)-Net over F₄ — Digital

Digital (113, 253, 165)-net over F₄, using

t-expansion [i] based on digital (109, 253, 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+140, 1287)-Net in Base 4 — Upper bound on s

There is no (113, 253, 1288)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 213 056882 837238 783844 612491 851787 882846 080060 552551 201008 572692 467917 323300 914989 081381 052439 115240 775505 072722 155629 234565 897243 915241 887223 228933 580180 > 4²⁵³ [i]