MinT - Best Known (118, 118+52, s)-Nets in Base 4

Best Known (118, 118+52, s)-Nets in Base 4

(118, 118+52, 312)-Net over F₄ — Constructive and digital

Digital (118, 170, 312)-net over F₄, using

t-expansion [i] based on digital (117, 170, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (117, 171, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 57, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(118, 118+52, 669)-Net over F₄ — Digital

Digital (118, 170, 669)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+52, 30367)-Net in Base 4 — Upper bound on s

There is no (118, 170, 30368)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 239855 763211 699078 478869 988041 646331 921246 128630 235514 130642 012941 251190 891211 853010 942110 165561 719855 > 4¹⁷⁰ [i]