MinT - Best Known (178, 178+56, s)-Nets in Base 4

Best Known (178, 178+56, s)-Nets in Base 4

(178, 178+56, 1036)-Net over F₄ — Constructive and digital

Digital (178, 234, 1036)-net over F₄, using

4² times duplication [i] based on digital (176, 232, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 58, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(178, 178+56, 2619)-Net over F₄ — Digital

Digital (178, 234, 2619)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 178+56, 404911)-Net in Base 4 — Upper bound on s

There is no (178, 234, 404912)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 762 145937 418967 997648 156094 148002 293095 461915 405344 288989 283578 178094 045510 871268 117318 265094 142985 802023 242884 144740 341913 792417 605610 791086 > 4²³⁴ [i]