MinT - Best Known (195−62, 195, s)-Nets in Base 4

Best Known (195−62, 195, s)-Nets in Base 4

(195−62, 195, 312)-Net over F₄ — Constructive and digital

Digital (133, 195, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 65, 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]

(195−62, 195, 643)-Net over F₄ — Digital

Digital (133, 195, 643)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−62, 195, 25329)-Net in Base 4 — Upper bound on s

There is no (133, 195, 25330)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2522 789530 536499 876458 445980 375649 184269 876561 488196 414839 404847 896787 107325 270243 851195 973761 233298 258125 566109 922992 > 4¹⁹⁵ [i]