MinT - Best Known (112, 112+76, s)-Nets in Base 4

Best Known (112, 112+76, s)-Nets in Base 4

(112, 112+76, 130)-Net over F₄ — Constructive and digital

Digital (112, 188, 130)-net over F₄, using

t-expansion [i] based on digital (105, 188, 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]

(112, 112+76, 267)-Net over F₄ — Digital

Digital (112, 188, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+76, 4736)-Net in Base 4 — Upper bound on s

There is no (112, 188, 4737)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 154586 636018 967356 252744 867963 195564 102550 213482 395162 782710 680082 988620 629607 525040 712024 517225 825700 503584 654144 > 4¹⁸⁸ [i]