MinT - Best Known (2, 2+5, s)-Nets in Base 128

Best Known (2, 2+5, s)-Nets in Base 128

(2, 2+5, 8128)-Net over F₁₂₈ — Constructive and digital

Digital (2, 7, 8128)-net over F₁₂₈, using

net defined by OOA [i] based on linear OOA(128⁷, 8128, F₁₂₈, 5, 5) (dual of [(8128, 5), 40633, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(128⁷, 8128, F₁₂₈, 4, 5) (dual of [(8128, 4), 32505, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
    - a code by Danev and Olsson [i]

(2, 2+5, 23352)-Net in Base 128 — Upper bound on s

There is no (2, 7, 23353)-net in base 128, because

1 times m-reduction [i] would yield (2, 6, 23353)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 4 398271 022212 > 128⁶ [i]