MinT - Best Known (123, 123+60, s)-Nets in Base 4

Best Known (123, 123+60, s)-Nets in Base 4

(123, 123+60, 240)-Net over F₄ — Constructive and digital

Digital (123, 183, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 61, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(123, 123+60, 542)-Net over F₄ — Digital

Digital (123, 183, 542)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+60, 18865)-Net in Base 4 — Upper bound on s

There is no (123, 183, 18866)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 408624 578506 275794 285693 109076 627615 215567 533556 699498 839400 002747 129999 481260 834028 821876 805038 586852 171568 > 4¹⁸³ [i]