MinT - Best Known (118, 172, s)-Nets in Base 4

Best Known (118, 172, s)-Nets in Base 4

(118, 172, 312)-Net over F₄ — Constructive and digital

Digital (118, 172, 312)-net over F₄, using

4¹ times duplication [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, 172, 608)-Net over F₄ — Digital

Digital (118, 172, 608)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 172, 24902)-Net in Base 4 — Upper bound on s

There is no (118, 172, 24903)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 845701 149450 236405 405949 633513 572436 916678 156164 100935 875318 507870 906508 924422 610526 771909 263305 429696 > 4¹⁷² [i]