MinT - Best Known (113, 113+134, s)-Nets in Base 4

Best Known (113, 113+134, s)-Nets in Base 4

(113, 113+134, 130)-Net over F₄ — Constructive and digital

Digital (113, 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]

(113, 113+134, 165)-Net over F₄ — Digital

Digital (113, 247, 165)-net over F₄, using

t-expansion [i] based on digital (109, 247, 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+134, 1370)-Net in Base 4 — Upper bound on s

There is no (113, 247, 1371)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52672 531367 326273 514489 048868 526940 672537 233727 399517 438237 982784 419734 288217 511901 527595 232593 780366 877417 059319 176457 436935 303251 166308 261325 292596 > 4²⁴⁷ [i]