MinT - Best Known (112, 112+89, s)-Nets in Base 4

Best Known (112, 112+89, s)-Nets in Base 4

(112, 112+89, 130)-Net over F₄ — Constructive and digital

Digital (112, 201, 130)-net over F₄, using

t-expansion [i] based on digital (105, 201, 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+89, 212)-Net over F₄ — Digital

Digital (112, 201, 212)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+89, 3100)-Net in Base 4 — Upper bound on s

There is no (112, 201, 3101)-net in base 4, because

1 times m-reduction [i] would yield (112, 200, 3101)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 602693 055808 387774 561658 995969 381696 316184 177385 928320 262338 072525 254489 367976 952771 617613 547786 290549 718326 515352 486944 > 4²⁰⁰ [i]